Introduction to Mathematical Statistics and Its Applications(4th Edition) | Date: 24 April 2011, 00:18
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Noted for its integration of real-world data and case studies, this guide offers sound coverage of the theoretical aspects of mathematical statistics. It demonstrates how and when to use statistical methods, while reinforcing the calculus that readers have already mastered. Presents standard statistical techniques in a mathematical context, allowing the reader to see the underlying hypotheses for the applications. Uses case studies and practical worked-out examples to motivate statistical reasoning and demonstrate the application of statistical methods to a wide variety of real-world situations. Discusses practical problems in the application of the ideas covered in each chapter, as well as common misunderstandings or faulty approaches. Revised Minitab sections now conform to the Version 14, the latest release. For anyone interested in learning more aboutmathematical statistics.
Summary: Well done
Rating: 5
I am surprised by the number of negative reviews for what I consider to be a nicely written, well thought out, and logically presented introductory course onmathematical statistics . Yes, a working knowledge of elementary calculus is a prerequisite. But the mathematics invoked in the exposition of concepts and theorems are kept as simple as possible while maintaining that modest level of rigor appropriate for a introductory exposition. If you do not have the minimal mathematical prerequisites (such as freshman calculus), blame your instructor or your school for selecting an inappropriate text. But don’t blame the authors! I thought the examples and problems were appropriate in their level of difficulty (mostly not so hard) and the relation to the material just covered. There are plenty of poorly written, impossibly dry, inpenetrable texts on statistics out there – this is not one of them. In addition, the book is attractively packaged, the paper quality is excellent, the visuals are informative and clearly presented – that also should not be taken for granted. Lastly the authors have a wicked entertaining sense of humor that spice the presentation throughout. I consider this book to be a welcome addition to the set of modern textbooks available to the curious serious student of probability and statistics.
Summary: dry and difficult
Rating: 3
In case you’re unclear on the matter, "mathematical statistics" is code talk for "statistics with calculus." So don’t think this is book is a high-school or even undergraduate-level "introduction" for statistics. For that I would recommend the friendlier but still meaty Stats: Modeling the World (2nd Edition) (DeVeaux/Velleman/Bock).
At my university, this book is usually used in the first math class required of those in graduate school majoriing in the statistical social sciences.
So make sure you’re ready. The authors assume you are quite solid at the calculus.
Summary: Confused and confusing
Rating: 2
I used this as the text in a sequence on probability and statistics I taught recently, and I soon came to regret this choice. The authors are obviously quite confused about basic concepts. Here are some examples: the "definition" of the median ignores obvious problems with existence and uniqueness; the "proof" of the central limit theorem is thoroughly incomplete; the "theorems" on the tests in Sect. 9.2, 9.3 summarize previous discussions, but the "proofs" of these theorems (we are even referred to an appendix – no small surprise when the statements seem obvious) establish something entirely different; finally, to conclude this (very incomplete) selection, there is the delightful claim that the golden ratio is a transcendental number (which just proves that the authors don’t have the slightest idea what a transcendental number really is, but then it might have been wise to avoid the use of the term).
In addition to these blatant problems, the authors’ treatment frequently misses the point and/or is confusing.
Summary: Infuriating
Rating: 1
The text presents all relevant information, but does so in such a confusing and poorly explained fashion as to prompt the reader to wonder if the authors have ever met anyone who hasn’t known all subtleties of probability since the womb. There is no avenue for the student who does not understand, no pedagogy whatsoever. Everything is presented at lightning pace with blisteringly difficult proofs and, often, no meaningful explanation of the physical meaning of the concepts explained. A very solid background in calculus is an absolute necessity, to the point where many problems in the text are more challenging in evaluating integrals than they are in actually applying concepts. This is a serious problem that recurs over and over.
Examples worked out in the chapter sections also almost never bear any resemblance to the problems students are expected to complete. Although the examples vary in terms of difficulty, a student stuck on an exercise almost definitely will not find any help in the teaching material of the section in completing it simply because the examples never entirely cover the concepts demanded in the exercises.
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Summary: Excellent intro to the mathematics of traditional statistics
Rating: 5
The first half of the book begins with basic discrete and continuous probability theory. It continues with thorough overviews of the basic distributions (normal, Poisson, binomial, multinomial, chi-squared and student-T). The focus is on basic probability and variance analysis, though it briefly covers higher-order moments.
The second half of this book is devoted to hypothesis testing and regression. There is an excellent explanation of the mathematical presuppositions of the various classical experimental methodologies ranging from chi-square to t-tests to generalized likelihood ratio testing. It contains a very nicely organized chapter on general regression analysis, concentrating on the common least squares case under the usual transforms (e.g. exponential, logistic, etc.).
Like many books in mathematics, this introduction starts from first principles in the topic it’s introducing, but assumes some "mathematical sophistication". In this case, it assumes you’re comfortable with basic definition-example-theorem style and that you understand the basics of multivariate differential equations. I was a math and computer science undergrad who did much better in abstract algebra and set theory than analysis and diff eqs, but I found this book extremely readable. I couldn’t have derived the proofs, but I could follow them because they were written as clearly as anything I’ve ever read in mathematics. I found the explanation of the central limit theorem and the numerous normal approximation theorems for sampling to be exceptionally clear.
The examples were both illuminating and entertaining. One of the beauties of statistics is that the examples are almost always interesting real-world problems, in this case ranging from biological (e.g. significance testing for cancer clusters) to man-made (e.g. Poisson models of football scoring) to physical (e.g. loaded dice). The examples tied directly to the techniques being explored. The exercises were more exercise-like in this book than in some math books where they’re a dumping ground for material that wouldn’t fit into the body of the text. This book has clearly been tuned over many years of classroom use with real students.
I read this book because I found I couldn’t understand the applied statistics I was reading in machine learning and Bayesian data analysis research papers in my field (computational linguistics). In paticular, I wanted the background to be able to tackle books such as Hastie et al.’s "Elements of Statistical Learning" or Gelman et al.’s "Bayesian Data Analysis", both of which pretty much assume a good grounding in the topics covered in this book by Larsen and make excellent follow-on reading.
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